>>11809276Physical objects (for ex the electro magnetic field) dont depend on the observer. Though their apperance does. For ex take a vector written in a Basis B
ie v=(v^i)(B_i) (einstein sum convention) now with a chosen basis B we can write v just as (v^1,v^2,...,v^n) because we know it refers to B. If we were to transform our Basis with a Matrix T into a Basis B‘
The components v^i transform with the inverse of T, that gives us:
v‘=v^i (T^-1)^j_i * (T)^k_j B_k = v^i (id)^i_k B_k = v^i B_i= v (where id is the identity matrix) as you can see allthough we transformed our reference frame, v didnt transform. BUT the new components ie with respect to B‘ are different namely v‘i=(T^-1)^i_j v^j
So our representation of v changes but the represntation i just that, the object stays invariant. Now in (special)relativistc QM we do exactly the same thing. Performing a lorentz transformation changes basis and components in such a way that the wavefunction (spinor) stays invariant but the apperance changes. This is why rel. QM is lorentz invariant and thus not observer dependent
